Event

I discuss work in progress on obtaining a reasonable density matrix of the universe in two dimensional quantum cosmology. I will do so by comparing aspects of the Hilbert space of closed universes in JT gravity, and in sine dilaton gravity. JT gravity is famously dual to a double scaled matrix model. In turn, sine dilaton gravity is dual to an ordinary finite cut matrix integral (this is more generally true for theories with a periodic dilaton potential). The duality with finite dimensional matrices relieves some of the issues with the density matrix of the universe in dS JT gravity. Ignoring topology change, the norm squared of the HH state in sine dilaton is finite (unlike in JT gravity) and matches the sphere computed in the matrix model. Including topology change, a quantum mechanical observer is to be added to avoid trivial quantum mechanics, both in JT and in sine dilaton gravity. With the observer, the density matrix of JT gravity remains non-normalizable (so it does not make sense). However, in sine dilaton gravity, one does obtain a finite density matrix. This stems from the finite size of the dual matrices. So, in this theory we can meaningfully ask for instance about the expected size of the universe.